Logic (2016)
16. Categories, Chapter 6 on Quantity: Intentions of the Mind, Number and the Unity of Piles
Class of 2017-01-12
https://berquistcourse.com/course/philosophy/2-logic-2016/016-categories-chapter-6-on-quantity-intentions-of-the-mind-number/

[0:00] Which where he says that the conception of the understanding. Look at it again, tripliciter, right? Adds itself to the thing which is outside the soul, right? This is a very famous distinction that Thomas gives a number of places. Sometimes what the understanding conceives is a likeness of a thing existing outside the soul, just as what is conceived by this name, man, right? And such a conception of the understanding has a foundation in the thing, what immediately, right?

[0:36] In so far as the thing itself, from its own conformity to the understanding, makes what is understood be what true, right? And the name signifying a thing understood properly is said of that thing, right? Sometimes, however, what the name signifies is not a likeness of a thing existing outside the soul, but it is something that follows from the way of understanding a thing which is outside the soul, right?

[1:08] And of this sort are the intentions which our understanding, right, introduces, right? Just as the signification of this name genus. Now we're back to the to the predicables, of Porphyry there, right.

[1:27] It's not a likeness of something outside the soul existing, right? But from this that the understanding understands animal as being in many what species, we attribute to animal the intention of what being a genus, right?

[1:47] And of this intention, although the proximate, right, the near, the close foundation is not in the thing, right, but in the understanding, right? Because outside the mind, animal is not separated from dog, cat, or elephant, right? Nevertheless, the remote foundation is in the thing itself, huh? Whence the understanding is not false, which introduces these what intentions, huh? And then he makes an interesting statement, which he doesn't develop right here.

[2:21] And similar about all the things which follow upon the way of what understanding, as is the abstraction of mathematical things and things of this sort, right? That's kind of funny. I was reading in Thomas today. He's talking about the power of God and rereading the De Potentia. and he's saying God cannot make the what genus not be said of the species. He can't make the genus not said of the species.

[2:51] He can't make number not said of seven. He can't make it animal not said of dog, right? That's pretty confining, right? To the immortal God, right? Amazing thing, right? Huh? But doesn't correspond to something outside, except in a remote way, right? There's a foundation in things, right? Huh? For animal to be separated, right, from dog and cat and horse in our mind. The foundation of the things is that they have something in common.

[3:21] Yeah, sometimes we say that the the genus is to the difference like matter is to form, right? Huh? And genus is not exactly the same thing as matter, because matter is a part of the thing, right? Huh? But it's taken one as material the thing, right? And then the difference from what is more the form of the thing, right? So there's a remote foundation, right, in the matter and form of these things.

[3:44] Um. But the immediate foundation is in our way of understanding these things, right? We understand things to be fused first, and then in general, right? Huh? But our mind separates out what they have in common, huh? Okay.

[4:01] But notice the last thing has to be developed some time, right? Just as the abstraction of mathematical things into the sort, and I told you about this disagreement that we have with I know as the editors of the Leonine, you know.

[4:18] Okay. When Thomas is commentary in the what, Proemium to the Nicomachean Ethics, right? Oh yeah. And there he speaks of how reason knows order, right? And he's going to distinguish the knowledge of reason by the order it considers, right? And he says, well, order is compared to reason in four ways. Okay. And of course Thomas there would seem to be violating the rule of two or three, right?

[4:46] But if you look at his words, he says there's an order which reason does not make, although it can consider this order. And then there's the order which reason itself makes, so that's the division of what two. And then the order which reason itself makes, he divides that into three, right? Now it's in comparison to reason he's doing this, right? So he says first the order which reason makes in its own acts, like the genus is before the difference on the definition, right?

[5:16] Okay. So the first thing you got to know about a square is that it's say what quadrilateral, right? And then that it's equilateral and right-angled, right? Okay. You got to

[5:31] know that a perfect number is a number before you know it's a perfect number, right? Okay. Then there's the order which reason makes in the acts of the will, right?

[5:43] So if virtue is the order to the road to happiness and vice is the road to misery, I want to you know acquire virtue so I'll be happy, right? Huh? Vice is the road to misery. And then there is the order which reason makes in what exterior matter, like in the table here, right? In the house or in the building, right? Okay, your clothing, so cloth.

[6:22] In mathematics you only have a remote foundation Well, it doesn't it doesn't unfold that here, right? Okay. Now he says, human art, mechanic arts, they call them, you know, the mechanical arts, the liberal arts, the civil arts are about the order which reason makes in exterior matter. The art of carpentry, right? The art of Christmas cookies. Oh my god quite great And then the art, the order which reason makes in the acts of the will, that's studied in what ethics and domestics and politics, right?

[6:58] Practical philosophy, and the order which reason makes in its own acts, in the thoughts and so on. the words that signify those thoughts, considered in logic, right? Then he says the order which reason does not make is the natural order, which is considered in natural philosophy. And then he adds, right? And metaphysics is also about order not made by our, what reason, right? I didn't make the order of the angels, right?

[7:25] Okay. He doesn't mention mathematics. What order that's about? Now some people say, well, Aristotle divides looking philosophy into what natural philosophy, mathematics, and and wisdom or first philosophy. And they had the famous treatise of, you know, of what? What's the name of the treatise on that same thing? A Boethius, right? Where he talks about this, huh? It's part of the part of the De Trinitate right Trinitate, right?

[8:00] Yeah, yeah. And he says they pull it out, you know, because it's a more fuller statement of what Aristotle brings out in the in the metaphysics. So Thomas must Thomas must mean then when he says this is the natural order is this this kind of work and wisdom is like that. He understands what's in the middle there, mathematics, right? So well, no, he he doesn't say it though, right?

[8:25] You know, why does he omit that, right? You know, it's so clear, right? Well, we point to this text, right? See, what does he mean here, huh? Okay. And similiter est de omnibus aliis quae consequuntur ex modo intelligendi, right? Just as the abstraction of mathematics things and things of this sort.

[8:51] Now I was reading a beautiful text in Thomas today, and you know God cannot make a square circle. Can't make something that involves a contradiction, right? When someone else, a little boy, you know, they used to try to challenge us Catholics. He said, "God is omnipotent, right? Can God make a stone so big he can't lift it?" And seems you're caught no matter which ones you say, right?

[9:28] But there's a contradiction saying a stone too big for God to lift. That involves a contradiction, you know. So God can't, you know, make something that involves a contradiction. Well, some people, of course, challenge that, right? And they say God can make something that's contradictory, right? He could make a square circle if he wanted to, right? But anyway, the argument that that is one of the objections there is very interesting, right?

[9:58] When God came, when Christ came the what the apostles after the resurrection, right? Huh? Or when he came, out of his mother's, you know. My mother always thought that was a wonderful thing, you know, because it's horrible to work to a child, right? I mean, it's really, really uncomfortable to say the least. And so when he spared his mother that thing, right? Most women, it's worse, I guess, because of the fall, right?

[10:27] Before the fall would have been as easy as as Tabitha, you know, when she was getting birth to those kittens, you know. Um. Uh. So um, when Christ came through the wall, right, where the apostles were cowering, you know, and so on. Um. Uh. Well, you know, in mathematics, right, huh? Between two points, can you draw two straight lines? You see this objection before? Between two points, you can't draw two straight lines, can you?

[11:05] Yeah. Yeah. Well, now, um. When two bodies are together, he had, you know, this point in my body and this point in the wall's body, right? When they're together, those two points, right? And two other points, right? Well, then you have two lines, right? Between what? Two points. Well, that's contradicting what we learn in geometry. So God can make contradictory things, right? Because he he didn't come through the wall, right?

[11:39] That's came through the tomb, you know. You know he wrote, resurrected, right? He didn't he didn't remove the stones. and say, let me out. Well, you know, could have rolled it back.

[11:50] Let him out. No, I think the church won't say that, right? So how can you get away with that? Ooh. Yeah. What Thomas says are not the same point, right? Because one point is in the body called the wall, the other point is in the body of Christ. So you got two points and two points, and so you don't have, you know, it's not the mathematical one, right?

[12:22] See, because the mathematical considers what line in separation from, as he says here, right? Yeah. Abstractio Mathematicorum, right? You see, So it's impossible in the abstract, you know, to have two lines between what two points? It's it could It could only be one line. But between two points in the body of Christ that coincide in place, right, with two points in the body of the wall, there could be what two different lines, right?

[12:52] Because one is in this body and one is in that body. It's kind of amazing thing, right? It's still miraculous in any ways. But I mean, it's not a contradiction with mathematics, right? So there's something strange about mathematics abstraction, right? You know, and something strange about mathematicians too. Something strange about mathematicians too. Yeah,

[13:19] yeah, yeah. Any times actually considers that objection somewhere? Yeah, I just got to be reading it in the. As a tendency, I guess. No, yeah, yeah, yeah. You see, subtle guy, Thomas, right? Okay Thomas, you see I always say text oublié you know, or forgot a text

[13:39] Something. So you've got to keep on reading these things. You find things, right? So at least all he said, you know, there's a question mark in your in your mind, right? Is the order right? He puts the order in mathematics apparently with the order in what? Logic. Yeah, not that they're the same. They're different sciences, right? And one is more in imagination, the other more in reason, right?

[14:02] But they are what? Not put with that first one, are they? So you got to be careful. Subtle, very subtle point. Okay. Okay. Now Aristotle, in this going all these problems here, right, in the categories, right, now, those kind of beginning things for people, right.

[14:41] Let's take this little text here from these sentences. To the theory, it should be said that aggregation. how would you translate aggregatio, Flocking together. Grex gregis You know, I don't know if other parishes have it, you know, but we have a little computer thing now where the the pastor can send us messages, right? And it's called I think it's called flocknotes yeah. It's kind of nice too.

[15:22] You see, you know, the the pastor went over to was it Rome, I guess. Yeah. No, no, he went to Palestine, right? You know, people in the parish, right now, and they send back, you know, to us from from the Holy Land pictures of the sites they were seeing, you know, and so on. Very, very nice way of sharing, you know, the trip of the. You can see the, you know, some of the parishioners, you know, and going with Father Rose, you know, and so on.

[15:49] So this is aggregatio, okay? And passions of this sort, right, which follow the what? Division of the continuous right, As Avicenna says in the third book of metaphysics, and it stands that this number is not in God right. So when you see that there are three persons in the blessed Trinity, did you divide something continuous into three? Because then these would be three parts of God right now, and God would no longer be what simple right.

[16:36] Another objection today that the second article is that whether God's power is infinite. Well, if it's infinite, then it has parts, and he's not simple. Because you have to understand what you mean by saying he's he's endless.

[16:54] To the fourth, it should be said that in absolute number there is a plurality which has a certain what composition and aggregation right. So in the number three there is what three ones are brought together right. It's a composed thing right. Well, how does Euclid define number right now? Multitude composed of ones right, something like that. And it's less certain than than one right. Which is its beginning right.

[17:30] And therefore not only as regards the understanding, but also as regards the thing itself, there is the measurability of the multitude of such a multitude by what one. So every number can be measured by one right.

[17:49] I'm counting right, okay. And so he says not only as regards the understanding, but also as regards the thing itself, there is a measurability of such multitude by unity. But in the number of relations, in the Trinity, right or persons, there is not some order of certitude that one is more certain right. Or, of composition in the thing.

[18:24] And therefore number in God, is not a multitude what measured them. Except perhaps according to the understanding only right, not in the thing, which composes right, but things that are not composed right, according as understands what

[18:49] them right. According to also it forms affirmative propositions right. These are all things here that are not maybe appropriate in studying the categories, but makes you stop and thinking of it. yeah. Now, look at the second in the text here from the sentences. Moreover, just as continuous quantity is made whole from its parts, right? So also number, right?

[19:32] But God, in divine things, there is a number of persons, right? This is the objection is saying To it. the third, Tenerius right? Of? Which one part is one, another part is two, right? Therefore, it seems that in God there is there a integral whole, yeah. Okay. I usually call integral whole a composed whole, but often they call integral whole right, as opposed to the universal whole, right? To the

[20:03] second, it should be said that in divine things, unity or duality is not a part of three, right? Except according to the way our reason takes it, right?

[20:19] Because, and the reason for this is because in another way there is number in the divine things, and in what created things, right? And in another way, what unity? For since the one is that which is undivided itself, and divided from others, each thing that is created, right, through its essence is distinguished from what others.

[20:56] For the essence itself, the thing created, according as it is undivided in itself and distinguishing from other things, is its unity, right? And many unities constitute a number of created persons.

[21:14] Just there are many essences congregated according to numbering, thus that there is nothing in one that is in another according to number the same, right?

[21:29] You and I, really two. Thus, number in created things has the notion of distinction, right, and of a certain piling up, huh, of things distinct in their essence. And from this, it has the notion of a what? Yeah. So I was teaching for centuries, things called classes, right? What were they, huh? Well, they were all distinct.

[22:09] Yeah, and they were piles you know just piles. And these piles. It's kind of funny this year. I've had twice in church, you know, at St. Mary's there, somebody come up to me that I had in class, you know, 20 years ago or 30 years ago or I don't know how many years ago, and they reintroduced themselves, you know, they said, "I thought it was you," you know, "I haven't seen you in church," and so it's kind of nice to come up, you know, but but they can see the heap, you know, that one heap after another, you know, that I taught, you know, or tried to teach anyone.

[22:42] Yeah, yeah, yeah. So thus, therefore, the number in things created has the notion of distinction and of a certain piling up of things distinct in essence. And from this it has the ratio of an integral whole, right? I I like the word composed whole, but it is the word integral. Now the personal unity, right, is the relative property, right, distinguishing one person from another, like the father from the son and the son from the father, and not the essence of the person.

[23:25] Whence the three persons are not differing by what essence, since one in number is the essence in the three what persons. The father and I are one, he said, right? I say about my own father, father, my father and I were one. Same nature. Yeah, yeah, but not one in number, right?

[23:51] And therefore there cannot be there a piling up, but only what distinction. Distinction. And account of this, the number does not have the notion of a integral whole or a composed whole, except perhaps in our mind, right? According as in reason are united the definitions, you might say, right, of the personal properties, right? Okay, there's three what properties there, right?

[24:26] But through this he says there's no integration of some thing, but in reason only, right? Now. And in this text, now another text here, Thomas speaks of the ones as not being simply one, and therefore a species if they are heaped up.

[24:58] Since they are composed from many unities, now this is more the creature I think he's talking about here. Either it is not one simply, but the unities are what flocked together by way of a what piling up, right? Which does not make something to be simply one, and consequently does not make constitute being in some species. Okay, now he's talking about something else here, then, right? And thus number is not some species of being.

[25:33] Or if number is one simply and not by it through itself, it should be said what makes it to be one from many unities, which cannot be assigned.

[25:45] Okay. Well, rest there. I have to think about that some more, huh? Dionysius, as Thomas explains, sees that number, even though it is in some way opposed to the one, partakes of what? Unity. Seven is one number. Yeah. Isn't it seven ones though? Yeah.

[26:19] He says that all things partake of one. He proves through this about which it would seem less to be so, to wit, by number, which in some ways opposed to one, as the divided is opposed to the undivided, right?

[26:38] For every number partakes one. Would the number be taken by itself, as it signifies when it said two or three? Or it what? Takes. Taken according as it names some part. Yeah. As when we name it as a half or a third or a tenth. Thomas explains that simply and properly, only those things which come together univocally in something one can be what? Yeah. So you and your chair

[27:17] two. Two natures, two things, but both existing. Yeah. We say that you're two. Two what? What do we have in common? Matter. See, two bodies, I guess.

[27:42] Although God and creature do not come together in something one according to some way of coming together, nevertheless one can consider the community of analogy between God and the creatures, in

[27:56] so far as creatures imitate Him, so far as they're evil, right? Whence, in some way, He can be numbered with other things, so that it be said that God and the angel are two things, right?

[28:10] Not, however, simply and properly, right? Hm. Just as creatures are. What? Numbered with each other. Yeah. Which come together univocally in something one, right? And from this it does not follow that God is a part of something, or that God and the angel are something greater than God, but that they are simply many things, huh?

[28:38] This raises incidentally the question whether number ten of the categories, or of highest genera, is a number which is a species in the category of quantity, for the ten genera do not come together univocally in something one.

[29:01] In another passage, Thomas adds, "To coming together in one species or genus, what comes together in some order, right? One existing which is in the genus of creatures is able to be numbered. That is, is a certain part of number. Everything that is one in creatures can be numbered with another which it comes together, either in species or in genus or in some order."

[29:35] That's rough stuff here. I'm subjecting you all to this sort of stuff. For many things existing in act do not come about one thing simply, unless there be something uniting and some way binding them together. To each other, right?

[30:08] Thus, therefore, if according to diverse forms, Socrates was an animal and rational, it would need two things that they be united simply, right? Something that would make them to be one. Whence, with this, since this is not able to be assigned, remains that man is not one except by what? Putting together. Yeah. Just as the pile, which is secundum quid unum, one pile, right? But simpliciter multa, right?

[30:42] There's a fallacy in the logic of fallacies and a fallacy of secundum quid and simpliciter right? Easily mix these up, these two, right? Now. And thus, man would not be a being simply, right? Because each thing, insofar as it is a being, insofar as it's one, right?

[31:12] So I'm a philosophical what? Grandfather, yeah. Or we can say I'm a a white philosopher. And a black man who is a philosopher because he's a black philosopher, right?

[31:29] Is that something a black philosopher or a white philosopher? You're looking at a white philosopher here, right? Is that something? Philosophical grandfather? Is there any way of becoming a white philosopher?

[31:57] I just happen to have Yeah. See, I was not always a white philosopher, right? So how did I become a white philosopher? I'm a Christian logician. You weren't always. I was not always a Christian. I was not always a logician, right?

[32:26] I got to be a Christian, I guess, by being baptized, huh? It's a good start. I got to be a logician by reading Porphyry and so Oesterle's logic.

[32:41] You know, this granddaughter there, she's she's in Fisher College now, right? So she's at Benedictine College there in Kansas. And her logic book was Oesterle's logic book, you know, which is kind of a famous one, right? But Oesterle, you know, didn't know how great a logician he was. But he's a good, good businessman. It's still, it's still, it's still a circulation, you know. You know, also his logic book.

[33:06] you know. Who's making that money now. Yeah. And you know his chapters, you know, different parts of logic, and he exercises in the book too, and so on. One that always sticks in my mind is, you know, he killed his daughter Ruth. Therefore, he is ruthless.

[33:25] It's kind of a clever thing, right? Some fallacy there, aren't you, Mister Lee? It's an equivocation there, right? He senses a ruthless son. Your argument is like an unsharpened pencil. It's pointless.

[33:59] Okay. In the seventh book of metaphysics, and according to this way, Democritus speaks rightly, saying that it's impossible for one to come to be from two, and from one to become two, right?

[34:22] It should be understood that two things existing in act never make one thing. But he, not distinguishing, that means Democritus, not distinguishing between potency or ability and act, laid down indivisible magnitudes to be the substances, right? The atoms, right?

[34:43] He wished that just as in that which is one there are not many in act, so also neither is there what in potency. And thus each magnitude would be what indivisible, right? So it is a straight line, one,

[35:04] or many. It's one in act, but it's many in what? Yeah, you could divide it, right? There's a theorem in geometry to divide a straight line, and you could divide those lines and so on, right? But for Democritus, didn't see that distinction of ability and act, right? So what did he have? Everything was. The atom. He's supposed to have given a what thought experiment? They call it Einstein.

[35:40] Suppose bodies were divided in every way they could be divided. What would be left? Well. Either there would be left these things that have no what size at all, right?

[36:03] Or there'd be nothing left, right? Well, it can't be nothing because you can't get something out of nothing. So if our bodies were divided in every way they could be divided, they would be just having what these atoms, these indivisible things. So this is thought experiment to make you think that everything is composed of these atoms, right? We see in the sunlight coming in, you know, and you know things moving around all the time, right?

[36:33] Okay. That's what he said, you know. These little ones, circular ones, there. You know. What does he have the problem there? If you if you cut a cone, right? Geometrically, how do you make a cone? You know, take a triangle, right? Then you rotate around a right angle, let's say, triangle, and rotate around, and you get a cone, right? Well, now if you cut a cone parallel to the base, right?

[37:05] And you look at up the bottom of the top part and the top of the bottom part, right? They're both circles, aren't they? Are they equal circles or unequal circles?

[37:20] What's equal? Well, if they're equal, then you're thinking of the cone as being what piled up of equal circles, right? Which would be not a cone but a what? Cylinder or something. Yeah, yeah. But if they're unequal, the circle at the bottom of the upper part and the top, then it's that's not straight down like a cone should be, right? So he had a problem there, right?

[37:48] Very subtle though these problems, huh? These Greeks. So Socrates would make you think about things, right? This way. I thank the gods for being born a man and not a woman, for being born a Greek and not a barbarian, and third for having met what Socrates. Okay. Now this is Democritus, another Greek. Yeah. For right,

[38:23] he says Democritus said, right? Supposing his position, by which he laid down that indivisible magnitudes to be the substances of things, right? And thus always they are in what acting, and thus from them there cannot come about what one thing, right? And thus, as it is in magnitude, so also in number, if number is a what putting together of units, right? As is said by some, is necessary either that duality is not something one.

[38:58] Or that what? Yeah. Or that unity is not in act in it, right? So are there really three ones and three, three, three actually distinct ones. It's really tearing your mind apart here, right now. As far as the categories are concerned, we know that you can divide being into what the ten, and you can divide quantity, discrete and continuous, and you can divide discrete into number and that, right?

[39:29] And we'll need this for more advanced parts of philosophy, right? You've got the fundamental divisions, right, to begin to get really into the difficult questions, right?

[39:42] And this duality will not be two units, but something from two units composed, right? Otherwise, number would not be something one per se and truly, but just as what things are piled up, right? So it's a pile. You got a pile of junk in your house, or like that, you know.

[40:04] the waste bear basket you know it's empty waste bear baskets on Thursday. you pick up the trash. And uh you had a bag of all this junk. And is that something one? That pile, that pile, pile of rocks. Is that something one? What would you say? In some way. Very secundum quid, though, right? Not some pile one, right? Huh? See. See.

[40:31] Sometimes you get the modern biologists talking about, you know, that each one of our cells is alive, so many, many lives, you know. Did you know you have as many lives as you have cells, right? Because each cell is alive, right, and and functioning. I mean, you know, occasionally some cells die, brush off some of these things, they probably died, right? You know, shave off some. But

[40:59] it's very hard to understand the unity of a number, right? Something one. Or is it a pile? In in the Trinity there, the three persons are one God, right? Not a pile of persons.

[41:27] People puzzle a lot about. Is it number one, right now? We study piles in arithmetic, or what? See. All these wonderful theorems that Euclid has, right? What are these? They got to

[41:48] be one in some way, per se, and truly, right? Otherwise, they'd be a pile Now, in the seventh book of the metaphysics here, Compositum, right? put together, sometimes gathers its species from something one that is a form, as is clear in a what mixed body, right? Huh?

[42:17] They found in the mixed body, right, that the what bodies mixed do not survive and act, right? Huh? But they're maybe one by a form. Or composition, as is clear in the house, right? I have one house. Or do I have a pile? No. Put together in some way, huh? Okay. That's more closer to the first meaning of composition, though, right?

[42:53] You know, should I say that I am composed in many ways, or I am put together in many ways? You know. See why Thomas has a whole article there, right? A whole question rather. Eight articles that God has not put together in any way.

[43:10] He distinguishes, as I said, how many kinds of being put together. About six ways, right? Or order. Okay. As is clear in the syllaba and numeral. See, that's going back to the distinction of what can discrete quantity, right?

[43:36] Shakespearean sonnet has fourteen lines. So this is one line, huh? From fairest creatures we desire increase, that thereby beauty's rose might never die. So,

[43:57] what do you mean, one line? That's a conglomeration of words and letters. A pile of letters. What what is what kind of unity does does a line of Shakespeare have? That's meter That's a kind of unity Yeah, there's an order in the line, right? See, the distinction of the syllables, and then there's an order. Yeah. Fair is foul, and foul is fair. Hover through the fog in filthy air.

[44:40] But he knows he puts that together, right? Syllaba? I guess. And what number, right? And then it's necessary that the whole composed is one Simpliciter, right? That's a great thing, huh? Sometimes the thing composed gets its species from some multitude of parts collected, as is clear in the pile and in the people, right? As of the sort. In such ones, the whole composed is not one simply, but one only according secundum quid.

[45:24] Now in this campaign they're both talking about bringing the country together, right? Uniting the country, you know, behind them. See, many would appreciate all this language, you know. I'm going to ask you a question about this unity that you're supposed to be seeking from the country. Is it simpliciter secundum quid? I see. I'm not taking your questions.

[45:58] Yeah.